10.6 polar coordinates

In addition to graphing points in terms of (x,y), we can also do so through (r,theta) . When we do this, his is called the polar coordinate system. R is the directed distance while theta is the directed angle. To express r, we generally draw circular rings around the origin. If the point is located on a further ring, we have a higher value if |r|. For instance of r =3, then the point will be located on the third ring. The exact location on the ring is determined by the angle. Theta is expressed through radians. We can use the angles on the unit circle to express the angles in the polar coordinate system. 

Now. How do we even convert (x,y) to (r, theta) and vice Versa?

To convert to (x,y)

X = r cos theta

Y= r sin theta

 To convert to (r,theta)

Tan theta = y/x

r^2=x^2+y^2

Now let's try to convert (3,pi)

X=3 cos pi = 3

Y = 3 sin pi = 0

(3,0) 

Congrats this is the main gist of section 6